Cook barley in a large pot of generously salted boiling water until al dente, 25 to 28 minutes. Drain; let cool 10 minutes. Meanwhile, heat a medium skillet over medium; swirl in 2 tablespoons oil. Add onion and carrots; season with salt and pepper. Cook, stirring occasionally, until onion is translucent and carrots are crisp-tender, about 5 minutes. Stir in ginger and coriander. Cook until fragrant, about 1 minute more. Transfer to a large bowl; stir in preserved lemon, olives, and lemon juice.

Stir barley into onion mixture. Stir in remaining 2 tablespoons oil; season with salt and pepper. Let cool about 1 hour, or cover and refrigerate up to 2 days. Stir in cilantro; serve.